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Hypergeometric representations of some mathematical functions via Maclaurin series. (English) Zbl 1474.33004

Summary: In this paper, by using Maclaurin series of a given mathematical function and expressing the coefficient of the general term of the corresponding Maclaurin series in form of Pochhammer symbols, we obtain the hypergeometric forms of following functions: \[ \frac{\sin^{-1}(x)}{\sqrt{(1-x^2)}},[\sin^{-1}(x)]^2,\sin^{-1}(x),\frac{\sinh^{-1}(x)}{\sqrt{(1+x^2)}},[\sinh^{-1}(x)]^2,\sinh^{-1}(x)\text{ and }\ln\{e(1-x)^{\frac{1}{x}}\}^{-\frac 2x}. \]

MSC:

33B10 Exponential and trigonometric functions
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